Calc 3 question - change of variables and computing the jacobian?

The problem asks to use a change of variables compute the double integral of y4dA over R, where R is the region bounded by the hyperbolas xy=1 and xy=4 and the lines y/x=1 and y/x=3.I was able to find that u=xy and v=y/x, and that u goes from 1 to 4 and v goes from 1 to 3. However, I can't compute the Jacobian determinant for the life of me! When I try to solve for x and y, I get expressions that have both u and v and x and y; I can't seem to isolate x and y. Please help me! Thanks.